powerpoint 1.ppt

Chapter 1

Introduction to Statistics

1Larson/Farber 4th ed.

Chapter Outline

• 1.1 An Overview of Statistics

• 1.2 Data Classification

• 1.3 Experimental Design

Larson/Farber 4th ed. 2

Section 1.1

An Overview of Statistics


Section 1.1 Objectives

• Define statistics

• Distinguish between a population and a sample

• Distinguish between a parameter and a statistic

• Distinguish between descriptive statistics and inferential statistics


What is Data?

Data

Consist of information coming from observations, counts, measurements, or responses.

• “People who eat three daily servings of whole grains have been shown to reduce their risk of…stroke by 37%.” (Source: Whole Grains Council)

• “Seventy percent of the 1500 U.S. spinal cord injuries to minors result from vehicle accidents, and 68 percent were not wearing a seatbelt.” (Source: UPI)


What is Statistics?

Statistics

The science of collecting, organizing, analyzing, and interpreting data in order to make decisions.


Data Sets

Population The collection of all outcomes, responses, measurements, or counts that are of interest.

Sample A subset of the population.


Example: Identifying Data Sets

In a recent survey, 1708 adults in the United States were asked if they think global warming is a problem that requires immediate government action. Nine hundred thirty-nine of the adults said yes. Identify the population and the sample. Describe the data set. (Adapted from: Pew Research Center)


Solution: Identifying Data Sets

• The population consists of the responses of all adults in the U.S.

• The sample consists of the responses of the 1708 adults in the U.S. in the survey.

• The sample is a subset of the responses of all adults in the U.S.

• The data set consists of 939 yes’s and 769 no’s.

Responses of adults in the U.S. (population)

Responses of adults in survey (sample)


Parameter and Statistic

Parameter

A number that describes a population characteristic.

Average age of all people in the United States

Statistic A number that describes a sample

characteristic.Average age of people from a sample of three states


Example: Distinguish Parameter and Statistic

Decide whether the numerical value describes a population parameter or a sample statistic.

1. A recent survey of a sample of MBAs reported that the average salary for an MBA is more than $82,000. (Source: The Wall Street Journal)

Solution:Sample statistic (the average of $82,000 is based on a subset of the population)


Example: Distinguish Parameter and Statistic

Decide whether the numerical value describes a population parameter or a sample statistic.

2. Starting salaries for the 667 MBA graduates from the University of Chicago Graduate School of Business increased 8.5% from the previous year.

Solution:Population parameter (the percent increase of 8.5% is based on all 667 graduates’ starting salaries)


Branches of Statistics

Descriptive Statistics Involves organizing, summarizing, and displaying data.

e.g. Tables, charts, averages

Inferential Statistics Involves using sample data to draw conclusions about a population.


Example: Descriptive and Inferential Statistics

Decide which part of the study represents the descriptive branch of statistics. What conclusions might be drawn from the study using inferential statistics?

A large sample of men, aged 48, was studied for 18 years. For unmarried men, approximately 70% were alive at age 65. For married men, 90% were alive at age 65. (Source: The Journal of Family Issues)


Solution: Descriptive and Inferential Statistics

Descriptive statistics involves statements such as “For unmarried men, approximately 70% were alive at age 65” and “For married men, 90% were alive at 65.”

A possible inference drawn from the study is that being married is associated with a longer life for men.


Section 1.1 Summary

• Defined statistics

• Distinguished between a population and a sample

• Distinguished between a parameter and a statistic

• Distinguished between descriptive statistics and inferential statistics


Section 1.2

Data Classification



• Distinguish between qualitative data and quantitative data

• Classify data with respect to the four levels of measurement


Types of Data

Qualitative Data

Consists of attributes, labels, or nonnumerical entries.

Major Place of birth Eye color


Types of Data

Quantitative data

Numerical measurements or counts.

Age Weight of a letter Temperature


Example: Classifying Data by Type

The base prices of several vehicles are shown in the table. Which data are qualitative data and which are quantitative data? (Source Ford Motor Company)


Solution: Classifying Data by Type

Quantitative Data (Base prices of vehicles models are numerical entries)

Qualitative Data (Names of vehicle models are nonnumerical entries)


Levels of Measurement

Nominal level of measurement

• Qualitative data only

• Categorized using names, labels, or qualities

• No mathematical computations can be made

Ordinal level of measurement

• Qualitative or quantitative data

• Data can be arranged in order

• Differences between data entries is not meaningful


Example: Classifying Data by Level

Two data sets are shown. Which data set consists of data at the nominal level? Which data set consists of data at the ordinal level? (Source: Nielsen Media Research)


Solution: Classifying Data by Level

Ordinal level (lists the rank of five TV programs. Data can be ordered. Difference between ranks is not meaningful.)

Nominal level (lists the call letters of each network affiliate. Call letters are names of network affiliates.)



Interval level of measurement

• Quantitative data

• Data can ordered

• Differences between data entries is meaningful

• Zero represents a position on a scale (not an inherent zero – zero does not imply “none”)



Ratio level of measurement

• Similar to interval level

• Zero entry is an inherent zero (implies “none”)

• A ratio of two data values can be formed

• One data value can be expressed as a multiple of another


Example: Classifying Data by Level

Two data sets are shown. Which data set consists of data at the interval level? Which data set consists of data at the ratio level? (Source: Major League Baseball)


Solution: Classifying Data by Level

Interval level (Quantitative data. Can find a difference between two dates, but a ratio does not make sense.)

Ratio level (Can find differences and write ratios.)


Summary of Four Levels of Measurement

Level ofMeasurement

Put data in

categories

Arrangedata inorder

Subtractdata

values

Determine if one data value is a

multiple of another

Nominal Yes No No No

Ordinal Yes Yes No No

Interval Yes Yes Yes No

Ratio Yes Yes Yes Yes


Section 1.2 Summary

• Distinguished between qualitative data and quantitative data

• Classified data with respect to the four levels of measurement


Section 1.3

Experimental Design



• Discuss how to design a statistical study

• Discuss data collection techniques

• Discuss how to design an experiment

• Discuss sampling techniques


Designing a Statistical Study

3. Collect the data.

4. Describe the data using descriptive statistics techniques.

5. Interpret the data and make decisions about the population using inferential statistics.

6. Identify any possible errors.

1. Identify the variable(s) of interest (the focus) and the population of the study.

2. Develop a detailed plan for collecting data. If you use a sample, make sure the sample is representative of the population.


Data Collection

Observational study

• A researcher observes and measures characteristics of interest of part of a population.

• Researchers observed and recorded the mouthing behavior on nonfood objects of children up to three years old. (Source: Pediatric Magazine)


Data Collection

Experiment

• A treatment is applied to part of a population and responses are observed.

• An experiment was performed in which diabetics took cinnamon extract daily while a control group took none. After 40 days, the diabetics who had the cinnamon reduced their risk of heart disease while the control group experienced no change. (Source: Diabetes Care)


Data Collection

Simulation

• Uses a mathematical or physical model to reproduce the conditions of a situation or process.

• Often involves the use of computers.

• Automobile manufacturers use simulations with dummies to study the effects of crashes on humans.


Data Collection

Survey

• An investigation of one or more characteristics of a population.

• Commonly done by interview, mail, or telephone.

• A survey is conducted on a sample of female physicians to determine whether the primary reason for their career choice is financial stability.


Example: Methods of Data Collection

Consider the following statistical studies. Which method of data collection would you use to collect data for each study?

1. A study of the effect of changing flight patterns on the number of airplane accidents.

Solution:Simulation (It is impractical to create this situation)



2. A study of the effect of eating oatmeal on lowering blood pressure.

Solution:Experiment (Measure the effect of a treatment – eating oatmeal)



Solution:Observational study (observe and measure certain characteristics of part of a population)

3. A study of how fourth grade students solve a puzzle.



Solution:Survey (Ask “Do you approve of the way the president is handling his job?”)

4. A study of U.S. residents’ approval rating of the U.S. president.


Sampling Techniques

Simple Random Sample

Every possible sample of the same size has the same chance of being selected.

x xx

xx

xx

x x

x

xx

xx

x

x x

xx

x

x

xx

xx xx x

xx

x

x

xxx

xx

x

x x

xx

x

x

xx

xx xx x

xx

x

x

xx

xx

x

x

x x

xx

x

x

xx

xx xx x

x x

x

xxx

xx

x

x x

xxx

x

xx

xx xx x

x x

x

x

x xx

xx

xx

x

x


Simple Random Sample

• Random numbers can be generated by a random number table, a software program or a calculator.

• Assign a number to each member of the population.

• Members of the population that correspond to these numbers become members of the sample.


Example: Simple Random Sample

There are 731 students currently enrolled in statistics at your school. You wish to form a sample of eight students to answer some survey questions. Select the students who will belong to the simple random sample.

• Assign numbers 1 to 731 to each student taking statistics.

• On the table of random numbers, choose a starting place at random (suppose you start in the third row, second column.)


Solution: Simple Random Sample

• Read the digits in groups of three• Ignore numbers greater than 731

The students assigned numbers 719, 662, 650, 4, 53, 589, 403, and 129 would make up the sample.


Other Sampling Techniques

Stratified Sample

• Divide a population into groups (strata) and select a random sample from each group.

• To collect a stratified sample of the number of people who live in West Ridge County households, you could divide the households into socioeconomic levels and then randomly select households from each level.



Cluster Sample

• Divide the population into groups (clusters) and select all of the members in one or more, but not all, of the clusters.

• In the West Ridge County example you could divide the households into clusters according to zip codes, then select all the households in one or more, but not all, zip codes.



Systematic Sample

• Choose a starting value at random. Then choose every kth member of the population.

• In the West Ridge County example you could assign a different number to each household, randomly choose a starting number, then select every 100th household.


Example: Identifying Sampling Techniques

You are doing a study to determine the opinion of students at your school regarding stem cell research. Identify the sampling technique used.

1. You divide the student population with respect to majors and randomly select and question some students in each major.

Solution:Stratified sampling (the students are divided into strata (majors) and a sample is selected from each major)


Example: Identifying Sampling Techniques

Solution:Simple random sample (each sample of the same size has an equal chance of being selected and each student has an equal chance of being selected.)

2. You assign each student a number and generate random numbers. You then question each student whose number is randomly selected.


Section 1.3 Summary

• Discussed how to design a statistical study

• Discussed data collection techniques

• Discussed how to design an experiment

• Discussed sampling techniques


powerpoint 1.ppt

Documents

population parameter

data setsthe population

data setsin

data classification1

sample statistic

data setspopulation

interpreting data

population characteristic